348 



Astronomical and Nautical Collections. 



sphere. Besides having apparently furnished to Newton an instru- 

 ment with which he has dazzled the admiring gaze of some later 

 philosophers, they exhibit also a remarkable specimen of a mode of 

 analysies which seems to afford a general if not a universal rule for 

 the integration of any given fluxion by induction : that is, to find 

 a series of successive fluxions of the given fluxinoal quantity, and 

 to express the relation of each term of this series to the pre- 

 ceding one in a general formula, which being applied to the first 

 term, or to the flexion itself, must naturally afford us the^wen^ 

 required. 



Parti. Brook Taylor, Nemton, Simpson, Kramp, and 

 Laplace, 



Translation of the 27th and last Proposition 0/ Taylor's Methodus 

 Incrementorum, 4. Lond. 1719. P. 108. 



Prop. XXVII. Probl. 



To fiiid the refraction of the light passing through the earth's 

 atmosphere. 



